The present invention relates to a method for analysis of a cell structure using a finite element method which is capable of efficiently and quickly determining the stress distribution which occurs inside the cell structure when a partial or nonuniform temperature change occurs inside the cell structure or when an external pressure is applied to the outer circumference (body face and end face) of the cell structure, and to a cell structure which has been subjected to stress analysis using the structural analysis method.
A honeycomb structure as an example of the cell structure has been used as a catalyst substrate for an exhaust gas purification device used for a heat engine such as an internal combustion engine or combustion equipment such as a boiler, a liquid fuel or gaseous fuel reformer, or the like. The honeycomb structure is also used as a filter for trapping and removing particulate matter contained in dust-containing fluid such as exhaust gas discharged from a diesel engine.
In the honeycomb structure used for such purposes, a nonuniform temperature distribution tends to occur inside the honeycomb structure due to a rapid temperature change or local heating of exhaust gas or the like, and pressure tends to be applied to the outer wall during canning. The stress which occurs inside the honeycomb structure due to the nonuniform temperature distribution or the external pressure may cause cracks to occur. In particular, when the honeycomb structure is used as a filter (diesel particulate filter: DPF) for trapping particulate matter contained in exhaust gas from a diesel engine, since the honeycomb filter is regenerated by burning and removing the deposited carbon particulate matter, a local increase in the temperature inevitably occurs. This increases the stress which occurs inside the honeycomb structure or on the outer wall (body face) or the end face, whereby cracks easily occur.
In general, it is desirable that the honeycomb structure used for the above-mentioned purposes have a wall thickness as small as possible. This is because the specific surface area can be increased when the honeycomb structure is used as a catalyst substrate and the air-flow resistance of exhaust gas or the like can be reduced when the honeycomb structure is used as a filter. However, since the structural strength is reduced as the wall thickness becomes smaller, judgment may be required as to whether or not the structural strength of the honeycomb structure having a predetermined wall thickness can withstand the stress which may occur under the use condition.
Conventionally, whether or not the honeycomb structure can withstand a predetermined stress has been confirmed by performing a use state simulation test using a method of increasing the temperature of the honeycomb structure in an electric kiln and thereafter immediately placing the resultant under normal temperature condition, a method of causing exhaust gas generated by burning diesel fuel using a burner to pass through the honeycomb structure and rapidly changing the temperature of the exhaust gas, a method of applying a hydrostatic pressure based on an isostatic strength test (Japanese Automobile Standards Organization (JASO) standard M505-87 published by Automotive Engineers of Japan, Inc.), or the like.
However, the above test method takes time, and poses limitations on possible test conditions. It is known that the stress which occurs in the honeycomb structure due to the internal temperature distribution or the external pressure may change depending on not only the wall thickness, but also the cell size, the property values of the constituent material, and the like. Therefore, development of a means for analyzing the stress distribution caused by the temperature distribution or the external pressure without performing a test has been demanded.
However, when applying a finite element analysis method for analyzing the stress distribution in the honeycomb structure, since the honeycomb structure has a three-dimensional structure in which many minute cells are assembled, the amount of calculation is increased to a large extent, and it is difficult to deal with such a large amount of calculation using commercially-available computer software and hardware. A supercomputer may perform such a calculation, but even that requires a long period of time. Moreover, such an investment increases the product cost, whereby competitiveness is weakened.
Prior art literature as to the means for analyzing the stress distribution inside the cell structure such as the honeycomb structure has not been found. As prior art literature dealing with a structural analysis of a structure in general, “Japan Society of Mechanical Engineers papers (A) Vol. 66, No. 642 (2000-2), paper No. 99-0312, pp. 14-20 (hereinafter called “non-patent document 1”)” proposes an efficient numerical analysis technique for a structure with local heterogeneity. In more detail, when analyzing a structure with local heterogeneity, it is necessary to determine not only deformation of the entire structure, but also the stress distribution near the heterogeneity, and the entire structure must be subdivided if modeling of the local region is given priority, whereby the data creation time and the calculation cost are increased to an impractical level. However, the non-patent document 1 suggests that this problem can be resolved by analyzing the local heterogeneity using a finite element mesh superposition method, and analyzing the remaining structure by a finite element method using a shell-solid connection in which the entire structure is modeled using the shell elements and the vicinity of the heterogeneity is modeled using the solid elements.
However, the means and the analytical example disclosed in the non-patent document 1 can be applied only when the region which requires a detailed analysis (local heterogeneity in the non-patent document 1 and the copper region in the tungsten plate in the analytical example) has been determined in advance. Therefore, it is difficult to apply the means disclosed in the non-patent document 1 as the means for analyzing the stress distribution which occurs inside the honeycomb structure used as a catalyst substrate or a filter when a temperature change occurs inside the honeycomb structure or pressure is applied from the outside. This is because the heterogeneity cannot be determined in advance since the stress distribution may change depending on the internal temperature change or the external pressure.